证据理论研究及其在矿井突水预测中的应用
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摘要
煤矿水害是矿井建设与生产过程中的主要灾害之一。突水事故给煤矿企业带来巨大的经济损失和人员伤亡。矿井突水预测是一个涉及水文地质、工程地质、开采条件、岩石力学等诸多因素的复杂问题。论文针对矿井突水这一不确定性和非线性灾害问题，建立了基于证据理论的矿井突水预测模型。主要对基于证据理论的信息融合技术在解决冲突证据、处理具有模糊性的对象和构建基本概率赋值函数等关键问题进行深入分析和研究，并利用改进的证据理论，融合矿井突水动态前兆信息，建立多场耦合的矿井突水预测模型，为矿井突水的可靠预测奠定理论和技术基础。
论文针对传统冲突系数识别证据冲突存在的不足，采用pignistic变换后得到的基本概率赋值函数之间的距离，结合传统冲突量化标准，讨论了Dempster组合规则适用条件，提出了一种改进的证据组合方法。该方法通过证据之间的pignistic概率距离表示证据之间的冲突程度，将证据间的冲突程度转化成相似程度，然后求出证据之间的支持程度，并确定权重系数，最后采用Dempster组合规则合成使用权重系数调整后的基本概率赋值。数值算例表明改进的方法不仅能够处理一般冲突，而且也能解决一票否决以及鲁棒性问题，并能使组合结果收敛到正确目标且收敛速度较快，这对改善信息融合系统的性能具有重要的意义。
获取基本概率赋值是应用证据理论解决工程问题最关键的一步，也是证据理论的核心问题。但由于证据理论应用背景的复杂性和多样性，使得寻求一种通用的构造基本概率赋值函数的方法一直难以较好地得到解决。论文基于广义三角模糊数，提出了一种通用的基本概率赋值构造方法。该方法利用样本数据的最小值、平均值和最大值构造单元素命题的三角模糊数表示模型，多子集命题的广义三角模糊数表示模型用单元素命题的三角模糊数表示模型的交叠部分来表示，通过广义三角模糊数的隶属度来构造基本概率赋值。该构造策略简单实用，易于计算，有广阔的应用前景。
由于传统证据理论无法处理具有模糊性的对象，论文利用证据理论和模糊集的优点来表示和处理不精确和模糊的信息，将证据理论向模糊集扩展。定义了一种新的模糊集贴近度计算方法。基于新的贴近度和模糊集分解定理，定义了模糊信任函数和模糊似然函数，其计算方法不受隶属度函数“关键点”的影响，能有效获取实际焦元变化信息，对焦元的微小变化也比较敏感；基于贴近度的模糊证据组合规则可有效地获取模糊焦元的变化信息，能够处理不确定和模糊信息，合成结果更有利于目标决策，这对扩大证据理论的应用范围具有重要意义。
从信息融合的角度，将本文提出的改进的证据理论应用到矿井突水水源识别和煤层底板突水量预测中，实验结果验证了本文提出的基于证据理论的矿井突水预测模型是可行的和有效的。最后，采用Windows7+Visual Studio2010Professional+SQL Server2008平台开发了基于证据理论的矿井突水预测系统，可为矿井提供准确、可靠的灾害预测，能有效提高了煤矿安全管理水平。
Water hazard in coal mine is one of the main disasters in mine construction andproduction. Water inrush disaster does enormous economic losses and casualties tocoal mine enterprises. Water inrush prediction in mine is a complex problem, as thewater inrush results from multiple effects of hydrogeology, engineering geology,mining condition, rock mechanics, etc. For resolving the uncertain and non-linearproblem of mine water inrush, a new model of a water inrush prediction in mine basedon evidence theory is put forward. The further study of the information fusion basedon evidence theory for combining conflict evidence, processing fuzziness object andconstructing basic probability assignment function are described in this dissertation.Based on the improved evidence theory, the dynamic precursory information of minewater inrush are fused, and the multi-field coupling model for water inrush predictionin mine is establish, which lay a foundation both in theory and technique for waterinrush prediction in mine.
To remedy the shortcomings in the recognition of evidence conflict by usingtraditional conflict coefficient, the application conditions of Dempster’s combinationrule are discussed by traditional conflict quantification standard and the distanceamong basic probability assignment functions transformed by pignistic. Furthermore,an improved method of evidence combination is presented. In this method, theconflict level is represented by the pignistic probability distance of evidence, after thatthe conflict level is transformed into similarity level and the support degree ofevidence is obtained. In addition, the weight coefficients are determined. Finally, thebasic probability assignments adjusted by weight coefficient are fused by Dempster’scombination rule. The numerical examples prove that the modified method not onlyhandle the evidence conflict efficiently but also solve the one-ballot veto androbustness problem, and has fast convergence speed. This is extraordinarilysignificant to improve the performance of the information fusion system.
Determination of the basic probability assignment is the core and key issue inevidence theory, and is the most difficult step in actual application. However, thegeneral way of determining the basic probability assignment has not appeared as theapplication background of evidence theory is complexity and diversity. Based on thegeneralized triangular fuzzy number, a general method for obtaining basic probabilityassignment is proposed in this dissertation. In the proposed method, the triangular fuzzy number described model of singleton proposition is constructed using theminimum, average and maximum values of the sample data. And the generalizedtriangular fuzzy number described model of multielement proposition is representedby the crossing area of the triangular fuzzy number described models of the singletonpropositions. Based on the degree of membership of the generalized triangular fuzzynumber, the basic probability assignment is obtained. This constructing strategy issimple, practical, and easy to calculation, has broad application prospects.
As incapable of disposing the fuzziness objects, evidence theory could begeneralized to fuzzy sets and the information about inaccuracy and fuzziness could berepresented and disposed by using the advantages of evidence theory and fuzzy sets. Amethod for defining the fuzzy closeness degree is put forward in this dissertation. Thefuzzy belief function and plausibility function are proposed on the basis of the newcloseness degree and fuzzy decomposition theorem. They are not influenced by somecritical points of the membership degree function, can gain the actual focal elementchange information effectively and are relatively sensitive to the subtle changes. Thefuzzy evidence combination rule based on fuzzy closeness degree can gain the changeinformation of the fuzzy focal elements effectively and dispose uncertain and fuzzyinformation effectively. The combination results are more conducive to objectivedecision. This is extraordinarily significant to expand the application range ofevidence theory.
As viewed from the perspective of information fusion, the methods of waterinrush source recognition and water inrush quantity from coal floor prediction areproposed based on evidence theory and its improved methods in this dissertation. Theexperiment results verify the feasibility and effectiveness of the water inrushprediction model. According to the improved methods, intelligent prediction systemof mine water inrush is developed on a Windows7, Visual Studio2010Professionaland SQL Server2008software platform which can provide accurate and credibledisaster prediction, and effectively improves the level of coal mine safetymanagement.
论文针对传统冲突系数识别证据冲突存在的不足，采用pignistic变换后得到的基本概率赋值函数之间的距离，结合传统冲突量化标准，讨论了Dempster组合规则适用条件，提出了一种改进的证据组合方法。该方法通过证据之间的pignistic概率距离表示证据之间的冲突程度，将证据间的冲突程度转化成相似程度，然后求出证据之间的支持程度，并确定权重系数，最后采用Dempster组合规则合成使用权重系数调整后的基本概率赋值。数值算例表明改进的方法不仅能够处理一般冲突，而且也能解决一票否决以及鲁棒性问题，并能使组合结果收敛到正确目标且收敛速度较快，这对改善信息融合系统的性能具有重要的意义。
获取基本概率赋值是应用证据理论解决工程问题最关键的一步，也是证据理论的核心问题。但由于证据理论应用背景的复杂性和多样性，使得寻求一种通用的构造基本概率赋值函数的方法一直难以较好地得到解决。论文基于广义三角模糊数，提出了一种通用的基本概率赋值构造方法。该方法利用样本数据的最小值、平均值和最大值构造单元素命题的三角模糊数表示模型，多子集命题的广义三角模糊数表示模型用单元素命题的三角模糊数表示模型的交叠部分来表示，通过广义三角模糊数的隶属度来构造基本概率赋值。该构造策略简单实用，易于计算，有广阔的应用前景。
由于传统证据理论无法处理具有模糊性的对象，论文利用证据理论和模糊集的优点来表示和处理不精确和模糊的信息，将证据理论向模糊集扩展。定义了一种新的模糊集贴近度计算方法。基于新的贴近度和模糊集分解定理，定义了模糊信任函数和模糊似然函数，其计算方法不受隶属度函数“关键点”的影响，能有效获取实际焦元变化信息，对焦元的微小变化也比较敏感；基于贴近度的模糊证据组合规则可有效地获取模糊焦元的变化信息，能够处理不确定和模糊信息，合成结果更有利于目标决策，这对扩大证据理论的应用范围具有重要意义。
从信息融合的角度，将本文提出的改进的证据理论应用到矿井突水水源识别和煤层底板突水量预测中，实验结果验证了本文提出的基于证据理论的矿井突水预测模型是可行的和有效的。最后，采用Windows7+Visual Studio2010Professional+SQL Server2008平台开发了基于证据理论的矿井突水预测系统，可为矿井提供准确、可靠的灾害预测，能有效提高了煤矿安全管理水平。
Water hazard in coal mine is one of the main disasters in mine construction andproduction. Water inrush disaster does enormous economic losses and casualties tocoal mine enterprises. Water inrush prediction in mine is a complex problem, as thewater inrush results from multiple effects of hydrogeology, engineering geology,mining condition, rock mechanics, etc. For resolving the uncertain and non-linearproblem of mine water inrush, a new model of a water inrush prediction in mine basedon evidence theory is put forward. The further study of the information fusion basedon evidence theory for combining conflict evidence, processing fuzziness object andconstructing basic probability assignment function are described in this dissertation.Based on the improved evidence theory, the dynamic precursory information of minewater inrush are fused, and the multi-field coupling model for water inrush predictionin mine is establish, which lay a foundation both in theory and technique for waterinrush prediction in mine.
To remedy the shortcomings in the recognition of evidence conflict by usingtraditional conflict coefficient, the application conditions of Dempster’s combinationrule are discussed by traditional conflict quantification standard and the distanceamong basic probability assignment functions transformed by pignistic. Furthermore,an improved method of evidence combination is presented. In this method, theconflict level is represented by the pignistic probability distance of evidence, after thatthe conflict level is transformed into similarity level and the support degree ofevidence is obtained. In addition, the weight coefficients are determined. Finally, thebasic probability assignments adjusted by weight coefficient are fused by Dempster’scombination rule. The numerical examples prove that the modified method not onlyhandle the evidence conflict efficiently but also solve the one-ballot veto androbustness problem, and has fast convergence speed. This is extraordinarilysignificant to improve the performance of the information fusion system.
Determination of the basic probability assignment is the core and key issue inevidence theory, and is the most difficult step in actual application. However, thegeneral way of determining the basic probability assignment has not appeared as theapplication background of evidence theory is complexity and diversity. Based on thegeneralized triangular fuzzy number, a general method for obtaining basic probabilityassignment is proposed in this dissertation. In the proposed method, the triangular fuzzy number described model of singleton proposition is constructed using theminimum, average and maximum values of the sample data. And the generalizedtriangular fuzzy number described model of multielement proposition is representedby the crossing area of the triangular fuzzy number described models of the singletonpropositions. Based on the degree of membership of the generalized triangular fuzzynumber, the basic probability assignment is obtained. This constructing strategy issimple, practical, and easy to calculation, has broad application prospects.
As incapable of disposing the fuzziness objects, evidence theory could begeneralized to fuzzy sets and the information about inaccuracy and fuzziness could berepresented and disposed by using the advantages of evidence theory and fuzzy sets. Amethod for defining the fuzzy closeness degree is put forward in this dissertation. Thefuzzy belief function and plausibility function are proposed on the basis of the newcloseness degree and fuzzy decomposition theorem. They are not influenced by somecritical points of the membership degree function, can gain the actual focal elementchange information effectively and are relatively sensitive to the subtle changes. Thefuzzy evidence combination rule based on fuzzy closeness degree can gain the changeinformation of the fuzzy focal elements effectively and dispose uncertain and fuzzyinformation effectively. The combination results are more conducive to objectivedecision. This is extraordinarily significant to expand the application range ofevidence theory.
As viewed from the perspective of information fusion, the methods of waterinrush source recognition and water inrush quantity from coal floor prediction areproposed based on evidence theory and its improved methods in this dissertation. Theexperiment results verify the feasibility and effectiveness of the water inrushprediction model. According to the improved methods, intelligent prediction systemof mine water inrush is developed on a Windows7, Visual Studio2010Professionaland SQL Server2008software platform which can provide accurate and credibledisaster prediction, and effectively improves the level of coal mine safetymanagement.
引文
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